Most computer-based design tools assume designers work with a well defined problem. However, this assumption has been challenged by current research. The explorative aspect of design, especially during conceptual design, is not fully addressed. This paper introduces a model for problem-design exploration, and how this model can be implemented using the genetic algorithm (GA) paradigm. The basic GA, which does not support our exploration model, evaluates individuals from a population of design solutions with an unchanged fitness function. This approach to evaluation implements search with a prefixed goal. Modifications to the basic GA are required to support exploration. Two approaches to implement a co-evolving GA are presented and discussed in this paper: one in which the fitness function is represented within the genotype, and a second in which the fitness function is modelled as a separately evolving population of genotypes.